Prospect Theory – A Beginner’s Guide

The following article appeared in the November 2016 issue of Equity published by the Australian Shareholder’s Association:

asa-equity-nov-2016

 

One of my favorite investment anecdotes is the story of the CGM focus fund – the best-performing US investment fund during the global financial crisis[1].

The fund returned an astonishing 18% per annum from 1999 through to 2009, beating its closest rival by more than 3%. Yet the typical CGM Focus investor lost -11% annually!

How can a fund earn 18% while the average investor earns -11%? To answer this question we need to first consider the difference between time-weighted and dollar-weighted investment returns.

Investment funds typically report time-weighted returns, that is the return calculations assume that the amount invested is constant over time. For example, many investment funds will present a chart showing the value of $1000 investment over time.

In reality, most investors vary the amount of their investment, adding or withdrawing funds over time. Dollar-weighted returnsincorporate the effect of cash flowing in and out of the fund as investors buy and sell.

Investor returns can be lower than investment fund total returns because investors often buy a fund after it has had a strong run and sell as it hits bottom. This is exactly what happened with the CGM Focus Fund.

The fund surged 80% in 2007. Investors poured $2.6 billion into CGM Focus the following year, only to see the fund sink -48%. Investors then yanked more than $750 million from the fund in the first eleven months of 2009.

The performance of the CGM focus fund is an extreme example of how emotions such as fear and greed can destroy wealth. It is also a vivid example of one of the cornerstones of behavioral economics – prospect theory.

We’ll come back to prospect theory a little later. But first, what is behavioral economics? Behavioral economics is the study of how people and institutions make economic decisions. For example, when we invest in a company’s shares we make both implicit and explicit judgments about the company’s future prospects. It’s worth pausing for a moment to think about what this involves: we are making decisions, in the face of uncertainty, with incomplete information; the results of which may not be known until several years in the future.

This doesn’t come naturally to most people, which is why all of us rely on mental shortcuts to make decisions. These shortcuts fall into two main categories:

  • Heuristics: People often make decisions based on approximate rules of thumb and not strict logic.
  • Framing: Our circumstances, past experiences, emotions, social factors and even the way in which choices are presented have a very large impact on our decisions.

Behavioral finance has identified many of the mental shortcuts that routinely trip up investors. We can improve the quality of our investment decisions by learning more about them.

Admittedly this may sound a little boring. After all, who wants to stop and think about howto make better decisions? That sounds like hard work. And it is. But it’s worth the effort.

There’s a very good reason why much of the investment industry and most of the media focus on how to find the next exciting growth stock or how to select the next “hot” sector of the market. It’s because they know that we’re highly likely to take the easy way out: rely on mental shortcuts to make decisions.

Learning to avoiding investment mistakes may never be as exciting as finding opportunities. But making fewer decision-making mistakes can materially increase our wealth.

Think about it this way, a good decision-making process provides a solid framework with which to make investment decisions and to control our behavioral inclinations. It helps to provide consistency and makes it easier to be a patient, long-term investor. We are also more likely to stick with our decisions as we will be making decisions that are in harmony with our financial goals.

How much better off financially would the investors in the CGM focus fund have been if they had such a framework?

The first step in building such a framework is to educate ourselves about the metal shortcuts that can get us into trouble. So with this in mind, we can now turn our attention back to prospect theory.

The modern history of behavioral finance began in 1979, when Daniel Kahneman and Amos Tversky wrote Prospect Theory: An Analysis of Decision Under Risk, an important academic paper that used cognitive psychology to explain how people make decisions when faced with uncertainty.

Up until that time, mainstream economics had assumed that people were completely rational: that is that they would always logically evaluate their options, decide and then act in a way that maximizes their utility or personal benefit.

Economists supported this view by theorizing that even if the assumption of rational thinking wasn’t always true, there would be enough self-interested and rational people (arbitrageurs) out there to identify the behavioral mistakes of irrational people as an opportunity to make money. They would then act on that opportunity. In other words, the market as a whole would act as if it’s rational due to arbitrage.

For example, it’s rational and logical to dislike losing money. Economists had long ago (Daniel Bernoulli in 1738) realized that people dislike gains more than losses. This is known as risk aversion.

They had also realized that context matters. For example, a gain of $100 is valued less by most people if they already have $10,000 (1% marginal gain) compared to when they only have $100 (100% marginal gain). This is commonly referred to in economics as diminishing marginal utility.

But the assumption of rationality could only explain so much. For example, it couldn’t explain why people responded differently to these two problems:

Problem 1: Assume yourself richer by $300 than you are today. You are offered a choice between:

  1. A sure gain of $100, or
  2. A 50% chance to gain $200 and a 50% chance to lose $0.

Problem 2: Assume yourself richer by $300 than you are today. You are offered a choice between:

  1. A sure loss of $100, or
  2. A 50% chance to lose $200 and a 50% chance to lose $0.

How did you choose? If you’re like most people, you would have chosen A for problem 1 and B for problem 2.

Here are the percentages of subjects choosing each option when tested:

Problem 1:

  1. 72%
  2. 28%

Problem 2:

  1. 36%
  2. 64%

Why does this matter? For both problems, the two choices have exactly the same expected value:

Problem 1:$100 = ($100 × 100%) and $100 = ($200 × 50%) + ($0 × 50%)

Problem 2:-$100 = (-$100 × 100%) and -$100 = (-$200 × 50%) + ($0 × 50%)

A rational person would be indifferent between the choices presented in each problem. Clearly this is not the case. Most people are significantly more likely to take the option that feels like a “sure thing” to protect a gain. They are also far more likely to choose the option that feels like “double or nothing” to avoid a loss.

The expected values are logically the same, but the choices feel different and that’s enough toinfluence our decision.

So what did the researchers find? In summary, they found that:

People are risk averse. Most people dislike losses approximately 2-3 times as much as they enjoy gains. This is commonly referred to in behavioural economics as loss aversion.

How people decide is heavily influenced by their starting or reference point. In other words, the way in which a choice is framed can make a huge difference. Framing a choice as a loss or as a gain is usually enough to bias most people’s decision-making. As we’ve seen, this bias is so powerful, it works even when there’s no logical difference between choices.

People will be risk-averse for gains but risk seeking for losses. This is exemplified by the two problems that we considered earlier. Most people will avoid risk by opting for the “sure thing” to protect a gain, even if it means giving up the possibility of making more money. Conversely they will seek risk by choosing the “double or nothing” gamble to avoid a loss.

People think about life in terms of changes and not levels. For example, the difference between losing $10 and $20 feels much bigger than the difference between losing $1,300 and $1,310. In either case the additional loss is $10, but in the first case the change is 100%, whereas in the second case, its only 7.7%.

Can prospect theory help us explain what happened to the average investor in CGM Focus fund? Yes it can:

2007 – The fund is up 80% while the S&P 500 is up only 4.42%. Investors have missed out (loss frame) on a spectacular gain. If only they had invested sooner! With no time to waste, investors pour $2.6 billion into the fund (risk seeking).

2008 – The fund is down-48%. The pain is almost unbearable, especially for new investors into the fund (losses hurt twice as much). Meanwhile, existing investors (gain frame) are watching their gains evaporate.

2009 – Investors can’t take it anymore. So they pull the plug and withdraw more than $750 million from the fund in the first eleven months of the year (loss aversion).

You may be wondering, why did investors pour $2.6 billion in but only take $750 million out? This can be explained by another implication of prospect theory – the disposition effect. But that’s a story for another day.

[1]Best Stock Fund of the Decade: CGM Focus, Wall Street Journal, December 31, 2009. http://www.wsj.com/articles/SB10001424052748704876804574628561609012716

 

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